As discussed in Chapter 2, the nucleons can be in different energy states in the nucleus (see the explanation of the shell model in Section 2.2.2). Therefore, the nucleons may be in excited states as a result of different nuclear processes. The excitation energy can produce the emission of a nucleon or radiation. The emission of a nucleon takes place in the nuclear reactions (Chapter 6), for example, in the (Y, n) nuclear reactions. As discussed in Section 4.4.6, the nuclei of the daughter nuclides can be in an excited state due to a radioactive decay. The excited nucleus may return to a lower excited state or ground state, emitting gamma photons with a characteristic energy.

The gamma photons can excite another nucleus. The cross section of this excita­tion process may be high when the energy of the gamma photon and the excitation energy of the nucleons are very close, for example, when the structure of the emit­ting and absorbing nuclei is similar, such as in the case of isobars, isotopes, or iso­ton nuclei. This process is called “nuclear resonance absorption.”

At first sight, the resonance absorption seems to be simple. However, the recoil of the nuclei during the emission and absorption reduces the energy of the gamma

Figure 5.26 The mass absorption coefficient for different gamma energies as a function of the atomic number of the absorbers.

photons (E0). The loss of energy (Er) can be calculated using the principle of the conservation of momentum:

—Mv = 0 (5.94)

c

where M is the mass of the nucleus, v is the velocity of the nucleus after the emis­sion of the gamma photon, and c is the velocity of light in a vacuum. By expressing the velocity of the nucleus after the emission of gamma photon, we obtain:

Eq_

Mc

The kinetic energy of the recoiled nucleus can be given as:

1 2 e2

Er = Mv2 = 0

Figure 5.27 Overlapping of absorption (left) and emission (right) photons. (A) In the case of gamma radiations, the lines do not overlap because of the high energy of recoil. (B) The overlapping of the emission and absorption lines at electron transmissions (optical spectra).

Besides the energy loss at the emission, gamma photons lose energy again when absorbed in the nucleus of the absorber. Therefore, the energy of the gamma pho­ton (E) after the absorption is:

E = E0 — 2Er (5.97)

As a result of the recoils of the two nuclei, the gamma photon does not have enough energy to excite the nucleus of the absorber. However, resonance absorp­tion can take place even if the gamma lines are so broad that the emission and absorption lines overlap (Figure 5.27).

The natural width of the lines (Г) can be calculated by the Heisenberg uncer­tainty principle:

h

Г t = — (5.98)

where t is the lifetime of the excited state. In nuclear processes, this lifetime is about 10-9—10-7 s, so the natural line width is very small (Figure 5.27, A). Furthermore, the atoms that are emitting radiation have different velocities because of the thermal movement. So, the frequency of each emitted photons (v) is shifted by the Doppler effect, depending on the velocity (v) of the atom relative to the observer:

where v0 is the frequency of the gamma photons when there is no difference in the velocities. Therefore, there is still some possibility of resonance absorption. As the temperature increases, the line width and the probability of the resonance absorp­tion increase.

191Os isotope (half-life, 15 days) emits beta particles, producing an 191mIr iso­tope. This excited nuclide falls into its ground state (191Ir) in 4.9 s, emitting gamma photons with 129 keV energy. Meantime, the nuclear spin decreases from +5/2 to +3/2. Mossbauer performed absorption experiments with this gamma radiation and iridium foil in 1958 and discovered the recoil-free resonance absorption of nuclei. Because he wanted to avoid resonance absorption, he did the experiments at very low temperatures. The unexpected result was that the resonance absorption increased enormously. At the first approximation, it is interpreted by the increased rigidity of the structure of the crystal lattice at low temperatures; i. e., the whole crystal can be considered to be a “recoiled atom.” So, the mass of the crystal can be substituted as M into Eqs. (5.95) and (5.96). As a result, the velocity and the energy of the recoiled atom will be negligible.

The recoil-free resonance absorption of nuclei can be used in the study of chem­ical states because the oxidation state and the chemical environment influence the energy state of the nucleus via the electrostatic interactions between the electrons and the nucleus. This change, called an “isomer shift” or a “chemical shift,” is by 7—8 orders of magnitude smaller than the characteristic energies of the nuclear pro­cesses. Therefore, a very small change of the very high energies has to be mea­sured. The isomer shift is measured using the Doppler effect: the resonance absorption is created by the relative movement of the sample (absorber) and the gamma radiation source. The relative velocity of the sample and the radiation source corresponds to the degree of the isomer shift, and its dimension is measured in cm/s or mm/s (for example). This small velocity correlates with the small differ­ences of the gamma energies caused by the different oxidation state or chemical environment of the Mossbauer nuclide in the absorber. The most important Mossbauer nuclides are 57Fe, 119Sn, 121Sb, 151Eu, 191Ir, 195Pt, 197Au, and 237Np.

The practical importance of the Mossbauer effect comes from the fact that one of the natural isotopes of iron, Fe-57 isotope, is a Mossbauer nuclide. The gamma radiation source is Co-57 (with a half-life of 9 months), the gamma radiation of 0.0144 MeV of which can excite the Fe-57 isotope. The decay scheme of Co-57 is shown in Figure 5.28.

The isomer shift of the different oxidation states of iron is illustrated in Figure 5.29 by the example of Fe(III) and Fe(II) fluorides. Figure 5.30 shows the Mossbauer spectrum of clay containing iron species.

As seen in Figure 5.29, the iron(III) in FeF3 is in a symmetrical environment and the electron configuration is 3d5, indicating high spin and the presentation of a singlet. The chemical environment of iron(II) in FeF2 is asymmetrical, with 3d6 configuration. The asymmetrical environment interacts with the electric quadrupole moment of the nucleus, resulting in the presentation of a doublet. At low tempera­tures, an inner magnetic field is formed, causing magnetic splitting (the Zeeman effect) with a sextet in the spectrum.

57 Q0 271 days

-7/2

	/ 0.1363MeV
0.1363 MeV у 11%		0.1219 MeV у 89% t 0.0144 MeV
	‘	! 0.0144 MeV у 0 MeV

EC 99.8%

-5/2

-3/2 0

57Fe

Figure 5.28 Decay scheme of Co-57.

v (mm s-1)

Figure 5.30 illustrates the Mossbauer spectrum of bentonite clay at 74 K before (A) and after (B) treatment with FeCl3 solved in acetones. Segment (A) shows the 12 and 13 oxidation states of iron in bentonite. The sextet in Figure 5.30B refers to the formation of a magnetic phase.